Larger Molecules / Longer Time Scales

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Larger Molecules / Longer Time Scales

• Todd J. Martinez

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Extending Quantum Chemistry

• Extend accuracy and/or size range of quantum
  chemistry?
• Remember the canon!

Right Answer
Minimal Basis Set Full CI
Minimal Basis Set/Hartree-Fock
Electron Correlation
Complete Basis Set/Hartree-Fock
Basis set
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Taking the Canon Seriously
Can we estimate the exact answer? Hypothesis
One- and Many-particle basis set
contributions to energy are additive Implies
that electron correlation and the flexibility of
the electronic wfn are independent cannot be
true Examples Gaussian-2 (G2) Complete Basis
Set (CBS)
These methods only work well when the SBS is big
enough to qualitatively describe
correlation, i.e. polarized double-zeta or
preferably better
Extrapolated Corr/LBS
Corr/SBS
G2/G3 Curtiss, et al. J. Phys. Chem. 105 227
(2001) CBS Montgomery, et al. J. Chem. Phys.
112 6532 (2000)
HF/SBS
HF/LBS
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Beyond the Canon
Can consider a 3-dimensional version of the canon
the new dimension is model size/faithfulness Fo
r example, consider the following sequence of
models
Should not ask about total energy, but rather
about energy differences, e.g. De(OH) in the
above examples. Always looking for ?E anyway
total energies are not experimentally observable
for molecules.
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Extending the Canon - IMOMO
Canon is now a cube

• Again, assume additivity

Ereal/LBS/Corr?Esmall/SBS/HF
(Esmall/LBS/HF-Esmal/SBS/HF)
(Esmall/SBS/Corr-Esmall/SBS/HF)
(Ereal/SBS/HF-Esmall/SBS/HF)

• Can be very sensitive to
• choice of small model
• Test thoroughly for your problem!

Vreven, et al. J. Comp. Chem. 21 1419 (2000)
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IMOMO Simplified

• If we lump basis set and correlation method
  together, we can just write

where high and low are the high-level and
low-level methods and real and model are
the target and truncated molecules
Example Proton Affinity See Lab this afternoon
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IMOMO Example
SN2 Reaction Energy
Re, et al. J. Phys. Chem. 105A, 7185 (2001)
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IMOMO Example
Errors of approx. 2 kcal/mol per solvent molecule
in absolute energies and 1-2 kcal/mol in
reaction energetics
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Multi-Level for Transition States?

• Simple variant of previous ideas
• Optimize w/low-level method (e.g. HF/3-21G)
• Energies w/high-level method (e.g. CCSD/cc-pvtz)
• Predict heat of reaction by difference of
  high-level E
• Why not do the same for TS?

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Why do Rxns have Barriers?
Its the electrons,
Simple example H2H?HH2
diabats, often reasonably approximated as
harmonic
VH H-H
VH-H H
Adiabatic PES w/barrier
Crudely approxd as constant
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Shift and Distort
To see the point, we need to complicate
things Consider XCH3 Y- ? X- H3CY

• Correlation and basis set
• affect frequency and
• relative energy of
• diabatic states

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Hope springs eternal

• It turns out that the MEP does not change much
• Determine MEP at low-level first
• Search along low-level MEP for maximum to get
• estimate for high-level barrier height IRCMax

High-Level
Low-Level
Malick, Petersson, and Montgomery, J. Chem. Phys.
108 5704 (1998)
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Empirical Valence Bond (EVB)

• Parameterize diabats and couplings
• One potential energy surface per bonding
  topology
• More potential energy surfaces, but advantage is
  that
• they are simpler than adiabatic surfaces
• Possible to incorporate solvent effects
• Disadvantages
• Diagonalize a matrix to get PES
• Number of diabats quickly gets large unless few
• reactions are allowed
• Proposed by Warshel and Weiss
• Recent applications Voth, Hammes-Schiffer,
  others

Warshel, et al. J. Amer. Chem. Soc. 102 6218
(1980) Cuma, et al. J. Phys. Chem. 105 2814
(2001)
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Large Molecules Directly

• Is there any way to solve electronic SE for
• large molecules w/o additivity approximations?
• O(N) Methods
• Divide and conquer
• Same ideas are applicable in ALL e- structure
  methods
• Generally harder to implement for correlated
  methods
• Available in commercial code (e.g. Qchem)
• Pseudospectral Methods
• Closely related to FFT methods in DFT and
  wavepacket dynamics

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Pseudospectral Methods-Intro
Integral Contractions are major bottleneck in
Gaussian-based methods
N4 work!
Try a numerical grid
2N3 work!
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Pseudospectral Methods
Problem grid pts scales w/molecular size, but
prefactor is usually very large Pseudospectral
Idea Dont think of numerical integration, but
of transform between spaces
R?spectral?physical
Q?physical?spectral
Q must be R-1
Least-squares fitting matrix
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Pseudospectral Performance

• PS advantage depends on Ng/N smaller is better
  
• Not useful for MBS/small molecules
• HF and Hybrid DFT, ?10x faster/100 atoms
• Advantage partly additive w/locality
• local MP2?30x faster/100 atoms
• Only available in commercial
• code Jaguar (Schrödinger)
• (accessible at NCSA)

Eg where PS-B3LYP optimization and PS-LMP2 energy
calculations are possible active site of
cytochrome c oxidase Moore and Martínez, J. Phys.
Chem. 104, 2367 (2000)
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Quantum Effects

• Is there any need for quantum mechanics of
  nuclei in
• large molecules?
• Answer not completely known, but certainly yes
  for
• Tunneling H transfer
• Electronic Excited States Photo-chemistry/biolo
  gy

• Classical mechanics only works with one PES?!

What should happen
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Traditional Methods
Need to solve TDSE for nuclear wavefunction

• Grid methods (Kosloff and Kosloff, J. Comp.
  Phys. 52 35 1983)
• Solve TDSE exactly
• Require entire PES at every time step
• Only feasible for lt 10 degrees of freedom
• Mean-Field (Meyer and Miller, J. Chem. Phys. 70
  3214 1979)
• Classical Mechanics on Averaged PES
• Problematic if PESs are very different

E
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Spawning Methods

• Classical mechanics guides basis set
• Adaptively increase basis set when quantum
  effects occur
• Best for t-localized quantum effects
• Effort ? N Classical Trajectories,
• size of N controls accuracy

Nuclear wavefunction
Electronic state
M. Ben-Nun and T. J. Martínez, Adv. Chem. Phys.
121, 439 (2002)
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Spawning Application

• Transmembrane protein
• 248 AA/7 helices
• Chromophore all-trans retinal
• 3762 atoms 11,286 DOF
• Light-driven proton pump

Light-induced isomerization
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bR Photocycle
Can simulate first steps directly
200 fs
lt 1ps
bR568
bR
J625
3-5 ps
5 ms
K590
O640
2 ms
ms
H
ms
70 ms
M412
L550
N520
H
Initial Geometry of RPSB
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Sample Results